![]() The reduction takes an arbi- trary SAT instance as input, and transforms it to a 3SAT instance. Solve SAT problems sequentially one at a time for horizon lengths 1, 2, 3, 4. If that's all the direction you need to get started, feel free to ignore the rest of this answer. SAT: A Simple Example Boolean Satisability (SAT) in a short sentence: SAT is the problem of deciding (requires a yes/no answer) if there is an assignment to the variables of a Boolean formula such that the formula is satised Consider the formula (ab)(ac) The assignment b True and c False satises the. We describe a polynomial time reduction from SAT to 3SAT. (Note that 3SAT itself is a decision problem, asking whether there is any solution). The decision version ("is there any integer solution to this set of equations") is the one that's equivalent to 3SAT. Recall that the Satisfiability problem is to decide, given a SAT formula (we will assume it is in CNF ), whether it is satisfiable (or consistent ) or not. The decision version just asks if there's any integer solution to the set of equations the optimization problem asks if there's a solution that optimizes/maximizes some objective function. There are two versions of the Integer Linear Program problem: a decision version and an optimization version. Of course, the 3CNF-SAT problem is simply this: given a formula in 3CNF, is there an assignment of values to the formulas variables for which the formula.
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